Proceedings of Sinn und Bedeutung 19. Edited by EVA CSIPAK (Georg-August-University Göttingen) HEDDE ZEIJLSTRA (Georg-August-University Göttingen)

Transcription

1 Proceedings of Sinn und Bedeutung 19 Edited by EVA CSIPAK (Georg-August-University Göttingen) HEDDE ZEIJLSTRA (Georg-August-University Göttingen)

2 Contents Introduction 1 Martin Aher & Jeroen Groenendijk: Deontic and epistemic modals in suppositional [inquisitive] semantics 2 Dorothy Ahn: The semantics of additive either 20 Stavroula Alexandropoulou: Testing the nature of variation effects with modified numerals 36 Curt Anderson: Numerical approximation using some 54 Jefferson Barlew: Coming to a doxastic agent 71 Corien Bary & Daniel Altshuler: Double access 89 Toni Bassaganyas-Bars: Have and the link between perfects and existentials in Old Catalan 107 Andrea Beltrama: From totally dark to totally old. The formal semantics of subjectification. 125 Andrea Beltrama & Jackson L. Lee: Great pizzas, ghost negations: The emergence and persistence of mixed expressives 143 Ivano Ciardelli & Floris Roelofsen: Alternatives in Montague Grammar 161 Elizabeth Coppock & Christian Josefson: Completely bare Swedish superlatives 179 Christopher Davis & Daniel Gutzmann: Use-conditional meaning and the semantics of pragmaticalization 197 Karen Duek & Adrian Brasoveanu: The polysemy of container pseudo-partitives 214 i

3 Allyson Ettinger & Sophia A. Malamud: Mandarin utterance-final particle ba (' ) in the conversational scoreboard 232 Nicole Gotzner: What s included in the set of alternatives? Psycholinguistic evidence for a permissive view 252 Julian Grove: Singular count pseudo-partitives 268 Daniel Gutzmann & Robert Henderson: Expressive, much? 286 Elena Herburger: Only if: If only we understood it 304 Roni Katzir & Raj Singh: Economy of structure and information: Oddness, questions, and answers 322 Natalia Korotkova: Evidentials in attitudes: do s and don ts 340 Helen Koulidobrova & Kathryn Davidson: Watch the attitude: Embedding and role-shift in ASL 358 Sven Lauer: Biscuits and provisos: Providing unconditional information by conditional means 377 Julia Lukassek: A single-event analysis for German eventive mit-modifiers 395 Melania S. Masià: Adjectives of veracity as vagueness regulators 413 Dejan Milačić & Raj Singh & Ida Toivonen: On the morphosyntactic representation of dependent quantification: distance distributivity, dependent indefinites, and Skolemization 431 Prerna Nadathur & Daniel Lassiter: Unless: an experimental approach 446 Miriam Nussbaum: Subset comparatives as comparative quantifiers 465 Doris Penka: At most at last 483 Agata Renans: Imperfective in Ga (Kwa) 501 Maribel Romero: High negation in subjunctive conditionals and polar questions 519 ii

4 Antje Roßdeutscher: Hidden universal quantification and change of argument structure in particle-verb constructions 537 Manfred Sailer: Inverse linking and telescoping as polyadic quantification 555 Florian Schwarz & Jacopo Romoli & Cory Bill: Scalar implicatures processing: slowly accepting the truth (literally) 573 Heiko Seeliger: Surely that s not a negative declarative question? Polar discourses in Swedish, German and English 591 Todd Snider: Using tautologies and contradictions 610 Benjamin Spector & Yasutada Sudo: Presupposed ignorance and exhaustification 628 Adrian Stegovec & Magdalena Kaufmann: Slovenian imperatives: You can t always embed what you want! 641 Robert Truswell & Nikolas Gisborne: Quantificational variability and the genesis of English headed wh-relatives 659 Yimei Xiang: A grammatical view of exhaustification with focus movement: Evidence from NPI-licensing 677 Erik Zyman: Lake Pátzcuaro P urhepecha and the semantic typology of degree constructions 695 iii

5 Introduction The present volume contains a collection of papers presented at the 19 th annual meeting Sinn und Bedeutung of the Gesellschaft für Semantik, which was held at the Georg-August-Universität Göttingen on September 15 th - 17 th, 2014 and which was jointly organized by LinG (Linguistics in Göttingen). 163 abstracts were submitted to SuB19; of the 52 talks of the program, 39 were elaborated into the papers in this collection, which appears online at: LinG - Linguistics in Göttingen & semanticsarchive.net The editors of the present volume would like to thank the authors for their contributions and all the anonymous reviewers for their collaboration. We also wish to thank our fellow organizers, Regine Eckardt, Paula Menendez-Benito, Edgar Onea, Igor Yanovich, our secretary Margitta Strüber, our student helpers, Nurcam Akcam, Ronja Brodhun, Benjamin Burkhardt, Paul Dijkzeul, Lea Fricke, Carina Kauf, Swantje Tönnis, Jessica Vaupel, Tanja Wiessner, all anonymous reviewers, the invited speakers, Ashwini Deo, Sabine Iatridou, Sophia Malamud and Ede Zimmermann (who could not be present) and all others involved for contributing to the success of this conference. Göttingen, July, Eva Csipak & Hedde Zeijlstra 1

6 AGrammaticalViewofExhaustificationwithFocusMovement: Evidence from NPI-Licensing 1 Yimei Xiang Harvard University Abstract. This paper offers an explanation to the NPI-licensing effect ofonly by incorporating focus movement into the grammatical view of exhaustification. The core assumption is that focus movement is motivated if interpreting focus in-situ yields ag-triviality/contradiction. Keywords: NPI, Focus movement, Exhaustification, Alternative Semantics, Only 1. Introduction It is well-known that the emphatic expression any is licensed as a (weak) negative polarity item (NPI) under downward-entailing (DE) contexts (Fauconnier 1975, 1979; Ladusaw 1979), such as under negation or in the left argument of a universal quantifier, as exemplified in (1) and (2), respectively. A context is DE if it supports a downward inference; for instance, observe in (3) that adownwardinferenceholdsfromasettoitssubsetintheleftargument of the universal quantifier every, butnotintheleftargumentoftheexistentialquantifiersome. (1) a. John didn t read any papers. b. *John read any papers. (2) a. Every student who has read any papers passed the exam. b. *Every student who has read some papers passed any exams. c. *Some student who has read any papers passed the exam. (3) a. Every student passed the exam.! Every smart student passed the exam. b. Some student passed the exam. 6! Some smart student passed the exam. The DE-based account is schematized as in (4), adopted from von Fintel (1999) and Gajewski (2007). 2 (4) a. An NPI is grammatical iff it appears in a constituent that is DE w.r.t. this NPI. b. A constituent A is DE w.r.t. a of type d iff the function lx.ja[a/v d ]K g[v d!x] is DE. [A[a/v] is the result of replacing a with v in A.] 1 For helpful comments and criticism, I want to thank Gennaro Chierchia, Noah Constant, Michael Erlewine, Danny Fox, Martin Hackl, Andreea Nicolae, Hedde Zeijlstra, and theaudiencesatlfrgatmit,glow37,andsub19for helpful suggestions and discussions. All errors in this workaremyownresponsibility. 2 standsforcross-categoricalentailment(vonfintel1999). (1) a. For p, q of type t: p q iff p is false or q is true. b. For f, g of type < s,t >: f g iff for all x of type s: f (x) g(x). In particular, for a, a 0 of type e: a a 0 iff for all P of type < e,t >: l P.P(a) l P.P(a 0 ). 677

7 c. A function f of type < s,t > is DE iff for all x and y of type s s.t. x y: f (y) f (x). Klima (1964) firstly observed that the exclusivefocus particle only can license NPIs. The emphatic expression any, forinstance,canbelicensedasannpiintherightargumentof NP-only or in the immediate scope of VP-only. Here and throughout the paper, I use CAPITAL letters to mark stressed items, and the F subscript to mark the semantic focus. (5) Right argument of NP-only a. Only JOHN F read any papers. b. *JOHN F read any papers. (6) Under VP-only a. Mary only gave any funding to JOHN F. b. *Mary gave any funding to JOHN F. One empirical constraint for the NPI-licensing effect of only is that NPIs cannot appear within the semantic focus or any focus (F)-contained island (Wagner 2006 a.o.). In particular, NP-only does not license NPIs in its left argument, as shown in (7); and VP-only, forinstance,cannotassociate with or into an anyp, as shown in (8): when VP-only directly associates with the determiner any, the entire DP any paper, orsimplythenpcomplementpaper,thenpiuseofany is not licensed. (7) *Only any students saw John. (8) a. *John only read ANY F papers. b. *John only read [any PAPERS] F,(hedidn treadeverybook). c. *John only read any PAPERS F,(hedidn treadanybooks). (8c) also illustrates the inviability of associating only into an NPI-contained island. According to Abels (2003), the complement of a phasal head (e.g. the D 0 any) cannotmovebyitselfand strand its embedding phrase head; it always pied-pipes its phasal head. Therefore, the anypin(8c) exhibits an island effect, to the extent that PAPERS cannot be moved out of the anyp. The remainder of this paper is organized as follows. Section 2and3willshowthatneither the F(ocus)-movement theory (Wagner 2006) nor the G(rammatical)-view of exhaustification can properly address the NPI-licensing effect of only by its own. Thus Section 4 will propose an alternative approach that incorporates features of both theories, built up upon an assumption that F-movement is motivated by the requirement of avoiding G-trivialities/contradictions. 2. The theory of F-movement 2.1. The SDE-condition The invalidity of downward inferences under only, firstlyindicatedbyatlas(1993),castsadoubt to Fauconnier-Ladusaw s DE-based account of NPI-licensing. While the right argument of NPonly and the non-f-associated part of VP-only are eligible positions for licensing weak NPIs, these contexts do not support downward inferences, as shown in (9). 678

8 (9) a. Only JOHN F ate vegetables for breakfast. 6! Only JOHN F ate kale for breakfast. b. John only ate VEGETABLES F for breakfast. 6! John only ate KALE F for breakfast. Given this problem, von Fintel (1999) proposes that S(trawson)DE environments are sufficient for licensing weak NPIs. The SDE condition, as schematized in (10), grants all presuppositions of the consequence when the validity of a downward inference is assessed. Further, von Fintel (1999) shows that only is an SDE function: the complement of only is DE when the prejacent presupposition is satisfied, as illustrated by the reasoningin(11). (10) A function f of type < s,t > is SDE iff for all x and y of type s such that x y and f (x) is defined: f (y) f (x). (11) Kale is a vegetable. x ) y John ate kale for breakfast. f (x) is defined Only John ate vegetables for breakfast. f (y) ) Only John ate kale for breakfast ) f (x) 2.2. Wagner (2006) Recall that only cannot license the NPI any when associated with or into the anyp. The SDE condition, nevertheless, still cannot capture the asymmetry between the F-associated part and the non-f-associated part in the scope of only. Toexplainthisasymmetry,Wagner(2006)adoptsthe SDE condition and proposes a theory of F(ocus)-movement. Wagner assumes that only has two syntactic arguments, a syntactic restrictor and a scope. In particular, only is SDE in its the scope but not in its restrictor. For instance, whentheprejacent presupposition of only is granted, a downward inference is supported in (12) but not in (13). only onlyp restrictor scope (12) Kale is a veg. John ate kale. Only JOHN F ate vegs. ) Only JOHN F ate kale (13) Graduates are students. Graduates ate kale. Only STUDENTS F ate kale. 6! Only GRADUATES F ate kale. Further, Wagner assumes that VP-only association invokes a covert phrasal movement of the focused expression to the restrictor of only. For cases where only associates into an island, he assumes that F-movementis island-sensitive (cf. Rooth 1985;among the others) and that the expressionundertakingf-movement is the minimalf-contained island (Drubig 1994). For instance, what gets F-movedin (14a)and (14)b shouldbe the complexdp and the when-clause, respectively. This assumption predicts an Island Restriction: Associationwithaconstituentwithinanislandcannot license an NPI in the same island. (Wagner 2006: 312) 679

9 Moreover, since F-movement is a phrasal movement, this assumption also predicts a Head Restriction: If only associates with the head of a constituent, it does not license an NPI in thecomplement of the head. Wagner (2006: ex. 42) For instance in (15), the F-moved element has to be the entire VP, including the anyp. 3 (14) a. Dr. Smith only rejected [the proposal that JOHN F submitted]. b. Dr. Smith only complains [when BILL F leaves the lights on]. (15) *John only CUT F any vegetables. This analysis immediately predicts that an NPI is not licensed in the immediate scope of VP-only if and only if this NPI appears within the F-moved constituent. This prediction is fully compatible with the observations with the VP-only in (6) and (8). In (6a), the focused NP moves alone to the restrictor of only, whilethenpiany stays and gets licensed within the scope part, as illustratedin (16a). As for the ungrammatical sentences in (8), in contrast, the NPI any is part of the F-moved constituent and therefore is not licensed, as illustrated in(16b). 4 (16) a. NPI is licensed b. NPI is not licensed only JOHN F,i VP Mary gave any funding to t i only DP i VP John read t i ANY F papers/[any PAPERS] F /any PAPERS F 2.3. Problems with the F-movement theory NPI-licensing condition Like the predecessors, Wagner (2006) does not explain why NPIs are not licensed in non-(s)de contexts; saying that NPIs must appear in (S)DE contexts is still a description. 5 What s more, 3 Jon Gajewski points out an insufficiency of this explanation to Wagner (2006: fn. 14): the object anypshouldbe allowed to vacate the VP, and the remnant VP subsequently associate with only. 4 In (8), the F-moved expression has to be the entire anyp, regardless of whether only associates with the entire anyporwithasub-componentoftheanyp. On the one hand, the D 0 any alone cannot take an F-movement, which is a phrasal movement. On the other hand, according to Abels (2003), the complement of D 0 cannot be moved out of the DP; therefore, when the NP complement of any is forced to take F-movement, the entire anyp gets F-moved. 5 Hsieh (2012) develops an explanation to the NPI-licensing effect of only based on Wagner (2006). But it inherits the problems of the SDE condition and Wagner (2006). 680

10 recent works on NPIs point out empirical problems with the SDE conditionandcriticizethatsde is neither necessary nor sufficient for NPI-licensing. On the onehand,ascrnič(2011)indicates, another prototypical F-sensitive expression exactly two can also license NPIs in its left argument, but exactly two is non-presuppositional and hence cannot be SDE; therefore the SDE condition is unnecessary for NPI-licensing. On the other hand, the SDE condition appears to be insufficient. For instance, the left arguments of DPs like the student and both students are SDE, but these positions do not license NPIs, as shown in (18) (Gajewski 2011, Chierchia 2013). (17) Exactly two students did any reading at all. (18) a. * The student who had any linguistics did well. i. Presupposition: students w =1 ii. Assertion:students w did well w b. * Both students who had any linguistics did well. i. Presupposition: students w =2 ii. Assertion:students w did well w Motivation of F-movement Wagner (2006) argues that only presupposes an 9-premise rather than the truth of its prejacent (Horn 1996, cf. Horn 1969). He schematizes the lexical entry of only as in (19), where the arguments f and P correspond to the syntactic restrictor/complement and the scope, respectively. The 9-presupposition (19b) abstracts over the entire complement of only. Accordingly,(20) and(21) have the same semantic focus but different 9-presuppositions. Here Wagner uses underlining to mark thesyntacticcomplement/restrictorofonly, pcorner symbolsq tomark thescopeofonly,and italics to mark the semantic focus. (19) a. JonlyK( f )(P) = 8a 2 C[P(a)! P( f ) P(a)] b. Presupposition: 9x.P(x) (20) With F-movement: a. John only pplayed basketballq. b. Presupposition: 9x. Johnplayedx. (21) Without F-movement: a. John only pplayed basketballq b. Presupposition: 9x. Johnx-ed. Next, adopting the Maximize Presupposition Principle from Heim (1991), Wagner assumes that F-movement is motivated to strengthen the 9-presupposition of only: F-movement minimizes the size the of the syntactic restrictor, which may have an effectonthestrengthofthestatementthatis grammatically encoded by the sentence. (Wagner 2006: 314) For instance, the 9-presupposition of only in (20) is stronger than the one in (21), motivating an F-movement. IarguethatthemotivationofF-movementandthesemanticsof only proposed by Wagner have two empirical problems. First, the semantics of only defined in (19) is too weak for cases like (22). It predicts (22) to be felicitous and true even if only John ate kale. To correctly predict the meaning of 681

11 (22), Wagner would have to assume that only presupposes not just an existential inference but also the truth of its prejacent. Such a move, however, would make the MP Principle inapplicable: the 9- presupposition, regardless of its strength, collapses under the prejacent presupposition; therefore, the F-moved form (20) would not be more preferable than the unmoved form (21). (22) Only [John and Mary] F ate kale. a. Presupposition: Someone ate kale. b. Assertion: Anyone who ate kale is part of John+Mary. Second, the assumed motivation of F-movement is incompatible with the basic example (15), repeated in (23). Accordingly, with or without F-movement, the syntacticcomplementofonly in (23) is always the entire VP, and the 9-presupposition is always (23a); therefore, if F-movement were used only to strengthen the 9-presupposition, it would NOT be motivated in (23). (23) *John only p CUT F any vegetablesq. a. Presupposition: 9x. Johnx-ed. b. Assertion: If John did any action to any vegetables, that action is no more than cutting. Further, a sentence of the form John only CUT F x isnotjustsdebutalsostrictdewithrespect to x: it is SDEbecause the downwardinference holds intheasserted part ((24a-ii) entails (24b-ii)); it is strict DE because the 9-presuppositions of (24a-b) are identical. 6 Therefore, Wagner cannot explain the ungrammaticality of (23), regardless of which NPI-licensing condition he adopts. (24) a. John only p CUT F vegetablesq i. Presupposition: John did something. ii. Assertion: If John did any action to vegetables, that action is no more than cutting. b. ) John only p CUT F kaleq i. Presupposition: John did something. ii. Assertion: If John did any action to kale, that action is nomorethancutting. In addition to the empirical problems, the 9-presupposition is defined unconventionally: it abstracts over the entire complement of only,not just the semantic focus(cf.horn 1996).To thisextent,the 9-presupposition is isolated from other major semantic properties of focus, such as the semantic focus or the quantificational domain, 7 which makes the lexicon of only quite inconsistent. 6 Wagner (2006: ex. 44b) himself writes the presupposition of (24b) as John did something with kale, which however conflicts with his main assumption that the existential import abstracts over the entire complement of only. 7 Wagner (2006) assumes that the semantic focus is obtained by contextually restricting the alternative set: alternatives to the entire syntactic complement are all considered; but the quantificational domain is contextually restricted, which helps to identify the semantic focus. 682

12 This inconsistency cannot be fixed under Wagner s basic framework. On the one hand, if the 9-presupposition is generated by abstracting over the semantic focus, its strength would not be affected by F-movement. On the other hand, if the quantificational domain is generated by abstracting over the complement of only,exhaustificationwouldleadtooverlystronginterpretations for sentences where only associates into an island. For instance in (25), due to the Left-Branch Extraction Constraint (Ross 1986), an F-movement theory requests the entire possessive NP JOHN s advisors to be F-moved. If the quantificational domain includes all the contextuallyrelevantindividuals,not just individualsthat are someone sadvisors, (25) would take the overly strong reading in (25b). (25) Sue only p invited JOHN F s advisors q. a.! Sue didn t invite anyone s advisors except John s advisors. b. 6! Sue didn t invite anyone except John s advisors Association with licensed NPIs Recall Wagner s prediction that an NPI is not licensed under only if it is part of the F-moved constituent. Conjoining this prediction with his claim that F-movement is mandatory for VP-only association, we get a stricter constraint stated as follows: VP-only cannot associate with an NPI or an NPI-contained island within which the NPI is not licensed. This constraint, however, is too strongfor cases like (26), where only associates with the anyp across another NPI-licenser(i.e.the clause-mate negation); the stricter constraint predicts (26) to take the LF in (27), under which the NPI any would not be licensed: the anyp, as the minimal F-contained island, would be moved to the syntactic restrictor of only, acontextthatisnon-sdeandcannotlicensenpis. (26) Mary only didn t give [any FUNDing] F to John. (She did her best to help him.) (27) [only (any funding) i [Mary didn t gave t i to John]] ( ) 3. The G-view of exhaustification 3.1. The G-view of scalar implicatures The G-view of exhaustification (Chierchia 2004; among the others) is firstly introduced to analyze scalar implicatures (SIs henceforth). This view argues that thephenomenonofsiisnotpurely pragmatic, based on the fact that SIs can be generated in embedding contexts. The main idea of the G-view is as follows. First, propositions containingscalaritemsareassociated with sets of alternatives, which are computed point-wise in the same way as the answer sets of questions (Hamblin 1973) and the alternative sets of focus (Rooth 1985, 1992). Next, 683

13 alternatives keep growing until factored into meaning via a covert exhaustivity operator O. The O- operator affirms the prejacent and negates all the alternatives that are not entailed by the prejacent, as schematized in (28). 8 Accordingly, an SI is a logic consequence of exhaustifying a sentence that contains a weak scalar item. For instance in (29), applying an O-operator over the some-sentence (notation: f SOME )affirmstheprejacentf SOME and negates the stronger alternative f ALL,yielding the implicature f ALL. (28) O(p)=p ^8q 2 ALT(p)[p 6 q! q] (29) a. Some of the students came. Not all of the students came. b. ALT(f SOME )={f SOME,f ALL } c. O(f SOME )=f SOME ^ f ALL 3.2. The G-view of NPIs Chierchia (2006, 2013) extends the G-view of SIs to the issue of NPI-licensing with assumptions compatible with the Alternative Semantics (Rooth 1985, 1992, 1996) and the strict DE condition. He proposes that the NPI any is an existential indefinite like some but encoded with a grammatical feature [D]. This feature obligatorily activates a set of domain (D)-alternatives and must be checked off by a c-commanding O D -operator. 9 Exercising an O D -operator over a sentence containing an occurrence of any has consequences in both syntax and semantics: in syntax, it checks off the [D] feature in the lexicon of any,justlikearegularfeature-checkingoperation;insemantics, it affirms the assertion and negates D-alternatives that are not entailed by the assertion. Consider the basic positive sentence (30) to see how the G-view captures the DE condition of NPIlicensing. With an indefinite 9-expression any, (30)asserts the 9-inference in (31b). Moreover, the [D] feature of any activates a set of D-alternatives, generated by substituting the total domain D with a subdomain D 0,asschematizedin(31c).Crucially,themonotonicitypattern of the entire clause with respect to the NPI any is upward-entailing (UE), and hence the proper D-alternatives are not entailed by the assertion. Last, applying O D negates all the proper D-alternatives, yielding 8 Here and throughout the paper, the symbols O and p are sloppily used for both syntactic phrases and truth conditions. A stricter semantic representation for O is as follows, where S is the immediate c-commanded phrase of O. (1) J O S K w,g = JSK(w) ^8S 0 2 ALT(S)[JSK 6 JS 0 K! JS 0 K(w)] 9 AschematicexampleforthetotaldomainD and its corresponding D-alternative sets is as follows. The the proper D-alternative set does not include the prejacent. (1) a. Total-D: {a,b} Assertion = 9x 2{a,b} f (x) b. Sub-D: {a,b},{a},{b} D-ALT = {9x 2{a,b} f (x),9x 2{a} f (x),9x 2{b} f (x)} c. Proper sub-d: {a},{b} Proper D-ALT = {9x 2{a} f (x),9x 2{b} f (x)} 684

14 the exhaustivity inference (31d), which however contradicts to the assertion (31b), as shown in (31e). This contradiction is the source of the ungrammaticality of (30). 10 (30) *John read any papers. (31) a. O D [John read any D papers] b. Assertion: 9x 2 D[P(x) ^ R( j,x)] (John read some papers in the total domain D) c. D-ALT = {9x 2 D 0 [P(x) ^ R( j,x)] D 0 D} d. 8D 0 [D 0 D! 9x 2 D 0 [P(x) ^ R( j,x)]] (for any proper subdomain D 0,JohnreadnopaperinD 0 ) e. J(31a)K = J(31b)K ^ J(31d)K =? (# John read some papers in D, buthereadnopaperinanypropersub-domaind 0 ) The contradiction in (31e) is essentially different from the onein(32). Theonein(31e)makes (30) ungrammatical, while the one in (32) makes the utteranceinfelicitousbutnotungrammatical. To tell them apart, Chierchia (2013) adopts the notions from Gajewski (2002) and describes the contradiction in (31e) as G(rammatical)-triviality, a special case of L(ogical)-triviality. 11 (32) # It is raining and it isn t raining. Under the G-view, the contradiction in (31e) can be avoided if theo D -operator is applied immediately over a constituent that is DE with respect to the NPI any. Consider the basic negative sentence (33) for example. By virtue of negation, all the D-alternatives are entailed by the assertion and therefore unexcludable. The O D -operator, although is mandatorily present for the sake of checking off the grammatical feature [D], is semantically vacuous. (33) John didn t read any papers. (34) a. O [John didn t read any D papers] 10 Consider the following mini model for a simpler illustrationofthisidea.assumethatthetotaldomaind contains exactly two items, paper p1 and paper p2. TheD-alternativeset is thus schematized as in (1b),containingexactly three elements: the asserted proposition John read a paper in {p 1, p 2 } and the proper D-alternatives including John read apaperin{p1} and John read a paper in {p2}. TheproperD-alternativesarenotentailedbytheassertion. Therefore, applying an O D -operator affirms the assertion and negates both proper D-alternatives, yielding the contradictory inference John read p 1 or p 2,andhedidnotreadp 1,andhedidnotreadp 2,asschematizedin(1c). (1) a. D = {p 1, p 2 } b. D-ALT = {R( j, p 1 ) _ R( j, p 2 ),R( j, p 1 ),R( j, p 2 )} c. R( j, p 1 ) _ R( j, p 2 ) ^ R( j, p 1 ) ^ R( j, p 2 )=? 11 L-trivialities are tautologies or contradictions in the traditional sense. While G-triviality means that a sentence receives the same value regardless of how the lexical terminals are replaced in the structure. For the purpose of this paper, it is enough to vaguely understand G-triviality as atypeofl-trivialityassessedatthegrammaticallevel. 685

15 b. Assertion: 9x 2 D[P(x) ^ R( j,x)] (John read no paper in the total domain D.) c. D-ALT = { 9x 2 D 0 [P(x) ^ R( j,x)] D 0 D} d. J(33a)K = J(33b)K = 9x 2 D[P(x) ^ R( j, x)] (John read no paper in the total domain D.) 3.3. Extending the G-view to only Krifka (1995), Lahiri (1998), and Chierchia (2013) extend the G-view of NPIs to the exclusive focus particle only. They adopt the lexical entry of only from Horn (1969), which assumes that only asserts an exhaustivity inference and presupposes the truth of its prejacent.the non-f-associated part of the asserted exhaustivity inference, crucially, is DE and hence is capable of licensing NPIs. Under the schematic notations in Chierchia (2013), the only-sentence (35) takes the LF in (36a). This LF has two exhaustification operators, O D and only, checkingoffthe[d]featureofany and the [F] feature of the semantic focus, respectively. The prejacent presupposition and the asserted exhaustivity inference are schematized as in (36b) and (36c), respectively. The D-alternatives are generated from the assertion by replacing the total domain D with a subdomain D 0,asin(36d). (35) Only JOHN read any papers. (36) a. O D [only [JOHN F read any D papers ]] b. Presupposition: 9x 2 D[P(x) ^ R( j,x)] (John read some paper in the total domain D.) c. Assertion: 8y 2 D e [9x 2 D[P(x) ^ R(y,x)]! j y] (For any individual y, ify read a paper in the total domain D, theny is John.) d. D-ALT = {only [JOHN F read any D 0 paper] : D 0 D } = {8y 2 D e [9x 2 D 0 [P(x) ^ R(y,x)]! j y] D 0 D} The presupposed component (35b), as firstly argued by Gajewski (2011) and extended by Chierchia (2013), is irrelevant for assessing the [D] feature of a weak NPI like any. 12 The asserted component (36c) is DE with respect to the non-f-associated part (underlined), where the NPI any appears. Therefore, the NPI any is licensed in (35), as it would be in any DE contexts. 12 Gajewski (2011) proposes that presuppositions and implicatures are relevant only for assessing the [D] feature of strong NPIs, not for that of weak NPIs. This proposal captures the contrast between weak NPI-licensing and strong NPI-licensing under only. Forinstance,only does not license the strong NPI in years in the non-f-associated part. (1) *Only JOHN came in years. The prejacent presupposition of only is purely UE, which, togethers with the asserted exhaustivity inference, makes the entire only-clause non-monotonic with respect to the strong NPI in years. Therefore,applyingO D to assess the [D] features in the presupposition and assertion yields a contradiction, making the strong NPI unlicensed. 686

16 In sum, the G-view provides an explanation to the DE condition of NPI-licensing: checking off the [D] feature of an NPI with a covert O D -operator yields a contradiction/g-triviality iff the O D - operator is applied immediately over a constituent that is non-de with respect to this NPI. As for case of only, the G-view shows that the assertion of an only-clause is DE in the non-f-associated part, which therefore gets (weak) NPIs licensed Problems with the G-view The G-view, however, is not the best solution. As a successor of Roothean Alternative Semantics, the G-view assumes that focus is interpreted in-situ and that F-alternativesarepropositional.For both NP-only and VP-only, theg-viewdefinestheirquantificationaldomainsasproposition sets. (37) JonlyK(p)=8q 2 ALT(p)[q! p q ] Nevertheless, the assumption that F-alternatives is propositional conflicts with the fact that only licenses weak NPIs. In (37), we can easily see that the boxed position for q is non-de. To be more accurate, consider a stricter schematic representation for the asserted component of the onlysentence (35). If the F-alternatives were propositional, then the asserted component of (35) would be schematized as follows. (38) 8q 2{9x 2 D[P(x) ^ R(y,x) y 2 D e }[ q! 9x 2 D[P(x) ^ R( j,x)] q ] Here the quantificational domain of only is characterized as a set of propositions in the form of y read a paper in the total domain D, where y is a contextually relevant individual. This schematic representation has three positions relevant to the assessment of the [D] feature (namely, containing an occurrence of any), each marked with a box. The first boxed position, as the restriction of a 8- quantification, is DE; but the latter two boxed positions, as within the scope of the 8-quantification, are UE. Therefore, under this representation, the entire assertion would be non-monotonic with respect to any, whichhoweverincorrectlypredictsthenpiany to be unlicensed in (35). Thus, to capture the NPI-licensing effect of only,theg-viewhastogiveupitsownconventionand write the quantificational domain of only as a set of individuals, as we have seen in (35c), where only the restriction part of the 8-quantification is relevant to the assessment of the [D] feature. 4. My analysis: grammatical view of exhaustification with F-movement Wrapping things up, neither the F-movement theory nor the G-view can properly address the NPIlicensing effect of only on its own. On the one hand, the F-movement theory is lacking of an explanation to the NPI-licensing condition. On the other hand, the G-viewdoes provide a plausible explanation to the licensing condition, but this explanation is viable only if the theory supports an operation (e.g. F-movement) that can split up the c-commanding domain of only and create a DE- 687

17 context. In such a case, a natural move would be to incorporate F-movement into the G-view. To integrate F-movement with the G-view, the only needed assumption is as follows (39) Motivation of F-movement The requirement of avoiding G-trivialities motivates F-movement. The rest of this section is organized as follows. Section 4.1 to 4.3 will focus on three basic cases. Case 1 covers sentences without NPIs or with NPIs that are licensed by operators other than only. Discussions on Case 2-3 will explain the NPI-licensing effect of only, inparticular,whyonly licenses NPIs, and why NPIs cannot appear within the semanticfocusoranf-containedisland.in section 4.4, I will move onto the so-called Head Restriction Case 1: F-movement is not motivated Under the motivation of F-movement assumed above, focus should be interpreted in-situ as long as interpreting it in-situ does not yield a G-triviality/contradiction. For instance in (40), the NPI any can be licensed in-situ by the clause-mate negation and hencethefocusdoesnotneedtomove. (40) Mary only didn t give any D funding to JOHN F Only O D not [Mary gave any D funding to JOHN F ] Under the present analysis, F-movement is not motivated in (41), because interpreting focus in-situ does not yield a contradiction. (41) Mary only didn t give [any FUNDing] F to John. She did her best to help him. When focus is interpreted in-situ, F-alternatives are propositional. The asserted meaning of VPonly can be schematized as in (42), à la Rooth Here p stands for the complement of VP-only. JpK f and JpK 0 correspond to the focus value of p and the ordinary value of p, respectively It is worthy of noticing that G-triviality is assessed at LF, therefore the rule (39) only applies to movement at LF, not to movement in the overt syntax. For instance, it is not thesourceoftheovertf-movementinhungarian. 14 Aquestionarisesastowhylogicalinferencesmotivatesyntactic operations. I would link this question to the architecture of the universal grammar. Chierchia (2006, 2013) indicates that the structure-building apparatus (e.g. Merge, Move, Agree) and the inferential one are not radically different; grammar only sees functional/logical material; logic sees functional/logical material and whether the lexical material is the same or different. (Chierchia 2013: 444) The notion of G-triviality, in particular, relates logic tightly to grammar, as a L-triviality taking effects in grammar. 15 The ordinary value of p is simply the truth value of p; thefocusvalueofp is a set of F-alternatives to p, builtup compositionally from the focus value of the semantic focus, defined as follows. (1) a. Ja F K f = D type(jak0 ) b. JaK f = {JaK 0 } c. Ja(b )K f = {a(b) a 2 JaK f,b 2 Jb K f } 688

18 (42) JonlyK(p)(w)=8q 2 JpK f [q(w)! JpK 0 q]=8q 2 JpK f [q(w)! p q] (Any true proposition within the focus value of p is entailed by the ordinary value of p.) Consider the example (25) again, repeated below. The quantificational domain of only is the focus value of the prejacent VP, namely a set of propositions in the form of Sue invited x s advisors. Exhaustifying over this domain yields the desired reading (43a), as schematized in (44). (43) Sue only invited JOHN F s advisors. a.! Sue didn t invite anyone s advisors except John s advisors. b. 6! Sue didn t invite anyone except John s advisors. (44) a. JSue invited JOHN F s advisork 0 = I[s,A( j)] b. JJOHN F K f = D e c. JSue invited JOHN F s advisork f = {I[s,A(x)] x 2 D e } d. J(43)K = 8q 2{I[s,A(x)] x 2 D e }[q! I[s,A( j)] q] (For any true proposition q in the form of Sue invited x s advisors, q is entailed by the prejacent that Sue invited John s advisors. ) 4.2. Case 2: F-movement is motivated Recall the main problem of the G-view: if F-alternatives were propositional, an only-sentence with an NPI would be non-de with respect to this NPI. Therefore, to capture the NPI-licensing effect of only in sentences like (45a-b), I assume that in those cases the semantic focus (or F-contained island, if any) has to be moved out of the VP, splitting the VP into two sub-constituents, namely the moved phrase, corresponding to the syntactic restrictor of only,andtheremnantvp,corresponding to the scope of only. In particular,to distinguish between VP-only and NP-only, I assume that F- movement is covert in (45a) but overt in (45b). (45) a. Mary only gave any funding to JOHN F. [O D [only(john F,i )[Marygaveany D funding to t i ]]] Covert F-movement b. Only JOHN F read any papers. [O D [only(john F,i )[t i read any papers.]]] Overt F-movement As for the semantics of only, IfollowAlternativeSemanticsandassumethatthequantificational domain of only is the focus value of the F-moved phrase. A cross-categorical definitionofonly is given in (46), where f and g correspond to the unmoved and moved part, respectively. (46) JonlyK( f <a,t> )(g a )=8g 0 2 JgK f [ f (g 0 )! JgK 0 g 0 ] For instance in (47), F-movement is motivated to avoid contradictions. The Left-Branch Extraction Constraint requests the F-contained island, JOHN F s advisors, tobemovedasawhole.thenthe 689

19 quantificational domain of only would be the focus value of the moved possessive NP, namely the set of contextually relevant individuals who are someone s advisors. (47) Mary only gave any D funding to JOHN F s advisors. a. JJOHN F s advisorsk f = {A(x) : x 2 D e } b. JJOHN F s advisorsk 0 = A( j) c. J(47)K = 8y 2{A(x) : x 2 D e }[I(s,y)! A( j) y] (For anyone s advisors y, ifmaryinvitedy, theny is/are John s advisors.) 4.3. Case 3: F-movement is unhelpful Recall the fact that only cannot directly associate with an NPI or with/into an NPI-contained island without crossing another NPI-licenser. Relevant examples discussed above are collected in (48). IwillshowthatthereasonwhyNPIsarenotlicensedinthethese examples is that F-movement cannot salvage their G-trivialities/contradictions. (48) a. *John read only ANY F papers. b. *John read only [any PAPERS] F,(hedidn treadeverybook). c. *John read only any PAPERS F,(hedidn treadanybooks). d. *Mary only gave a book to John [because BILL F gave any book to him]. Consider (48b) for example, where only associates with the entire anyp. To pursue a stipulationfree analysis, I will consider all possible syntactically well-formed LFs, including LFs where the [D] feature of any is assessed by a covert O D,aswellasLFswherethe[D]featureisassessedby overt only,asstructuredin(49)and(50),respectively. (49) Assessing [D] with O D a. O D [only [John read [any D PAPERS] F ]] Without F-movement b. O D [only (any D PAPERS) F,i [John read t i ]] With F-movement (50) Assessing [D] with only a. only [John read [any D PAPERS] F ] WithoutF-movement b. [only (any D PAPERS) F,i [John read t i ]] With F-movement Let us start with the option that only the covert operator O D can assess a [D] feature. If the anyp is interpreted in-situ, as in (51a), then the [D] feature of any would be assessed within the boxed part, which is within the scope of a 8-quantification and is non-de. Then applying O D over the only-clause to check off the [D] feature would yield a semantic contradiction. Alternatively, if the focused anypisf-moved,itwouldbeinterpretedundertheimmediatescope of O D,acontextthat 690

20 is also non-de. The main difference between (51) and (52) in semantics is that the quantificational domain of only is a set of propositions in (51) but a set of generalized quantifiers in (52). 16 (51) a. O D [only [John read [any D PAPERS] F ]] b. Assertion: 8q 2{Q(lx.R( j,x)) Q 2 D <et,t> }[q! 9x 2 D[P(x) ^ R( j,x)] q] (52) a. O D [only (any D PAPERS) F,i [John read t i ]] b. Assertion: 8Q <et,t> [Q[ly.R( j,y)]! ls.9x 2 D[P(x) ^ S(x)] Q] Now move onto the option that the overt exclusive particle only can check off any alternativerelated features, including the [D] feature. In such a case, the O D -operator ought to be eliminated from the LF of a only-sentence, because there is no unchecked [D] left for O D.Thisoptionhasnot been considered by the canonical G-view. But in theory, thereisnoreasontoruleitout. First, consider the possibility of interpreting anyp in-situ. Under the LF(53a), the only-sentence presupposes its prejacent as in (53d) and asserts the exhaustivity inference as in (53e). The quantificational domain of only consists of F-alternatives and D-alternatives: F-alternatives are in the form of John read X, where X is a generalized quantifier; D-alternatives are in the form of John read a book in D 0, where D 0 is a subset of the total domain D. Theassertedexhaustivityinference entails the negation of all the proper D-alternatives, yielding the inference John didn t read any paper in any proper subdomain D 0,asin(53f).Thisinference,however,contradictstheprejacent presupposition John read a paper in the total domain D,predictingtheNPIany to be unlicensed. 17 (53) a. only [John read [any D PAPERS] F ] b. ALT F = {Q[lx.R( j,x)] Q 2 D <et,t> } c. ALT D = {9x 2 D 0 [P(x) ^ R( j,x)] D 0 D} d. 9x 2 D[P(x) ^ R( j,x)] Presupposition e. 8q 2 ALT F,D [9x 2 D[P(x) ^ R( j,x)] 6 q! q] Assertion f. )8D 0 [D 0 D! 9x 2 D 0 [P(x) ^ R( j,x)]] (John didn t read any paper in any proper subdomain D 0 ) 16 Individuals of type e can also be type-shifted into generalized quantifiers. 17 Consider the mini-model below for a simpler illustration of (53). Assume that the total domain D contains exactly two papers, p 1 and p 2.TheD-alternativesetthuscontainsthreepropositions,John read p 1 or p 2, John read p 1,and John read p 2,asin(1b).Theexhaustivityassertionnegatesbothpropersub-D alternatives, yielding the inference John didn t read p 1 or p 2 in (1c), which contradicts the prejacent presupposition John read p 1 or p 2 in (1d). (1) a. D = {p 1, p 2 } b. D-ALT = {R( j, p 1 ) _ R( j, p 2 ),R( j, p 1 ),R( j, p 2 )} c. Assertion entails: R( j, p 1 ) ^ R( j, p 2 ) d. Prejacent Presupposition: R( j, p 1 ) _ R( j, p 2 ) 691

21 This reasoning also applies to the LF in (54), where the anyptakescovertf-movementtothecomplement of only: theexhaustivityassertionin(54e)entailstheinferencein (54f), which contradicts the prejacent presupposition in (54d). The major difference betweentheschematicderivationsin (53) and (54) is the semantic type of their alternatives: in (53), all the alternatives are propositions; but in (54), all the alternatives are generalized quantifiers. In particular, the D-alternatives in (54c) are existential quantifiers quantifying over papers in a subset domain D 0. (54) a. [only (any D PAPERS) F,i [John read t i ]] b. ALT F = D <et,t> c. ALT D = {ls.9x 2 D 0 [P(x) ^ S(x)] D 0 D} d. 9x 2 D[P(x) ^ R( j,x)] Presupposition e. 8Q 2 ALT F,D [Q 6 ls.9x 2 D[P(x) ^ S(x)]! Q[ly.R( j,y)]] Assertion f. )8D 0 [D 0 D! 9x 2 D 0 [P(x) ^ R( j,x)]] (John didn t read any paper in any proper subdomain D 0 ) To sum up, if only associates with an anyp, all the syntactically well-formed LFs of (48b) yield a G- triviality; therefore the NPI any is not licensed in (48b). First, if the [D] feature of any is assessed by a covert O D,thentheG-trivialitywouldbealogicalconsequenceoftheaffirmed exhaustivity assertion and the negated proper D-alternatives. Second, if the[d]feature is assessed by overt only, then the G-triviality would result from the contradiction between the prejacent presupposition of only and the negation of the proper sub-d alternatives The Head Restriction The present analysis can easily capture the Head Restriction. In (55), although the anyp can vacate from the VP before the [D] feature gets assessed, it can andcanonlyberaisedtotheplace sandwiched between O D and only,whichisstillnon-de.incontrast,theconditional(56)isde in its antecedent; therefore, once the anyp undertakesqroveronly, thewholeconditionalwouldbe DE with respect to the NPI. (55) *John only CUT F any vegetables. [O D [any D vegs] i [only[johncut F t i ]]] (56) If John only CUT F any vegs (and didn t STEAM F any vegs), Mary would be unhappy. Note that the NPI any is not licensed once if the anyp cannottakequantifierraisingoveronly, even if the only-sentence is uttered as the antecedent of a conditional or in some other DE context. For instance, the NPI any is not licensed in (57), a conditional where only associates into an anyp. First, the determiner any cannot take F-movement alone, ruling out the possibility in (57a). Second, since an only-associated focus cannot be moved from beneath only (Tancredi 1990), the F-contained anypcannotraiseoveronly, rulingoutthepossibilityin(57b). 692

22 (57) *If John only invited [anyone s ADVISORS F ], the students would be unhappy. a. If John only invited anyone s ADVISORS F,... ( ) b. If John only invited anyone s ADVISORS F,... ( ) 5. Conclusions The goal of this paper has been to explain the NPI-licensing effect of only. I incorporated F- movement into the G-view of exhaustification with a simple assumption that F-movement is motivated by the requirement of avoiding contradictions. References Abels, K. (2003). Successive cyclicity, anti-locality, and adposition stranding. Ph. D. thesis, University of Connecticut. Atlas, J. D. (1993). The importance of being only : Testing the neo-gricean versus neo-entailment paradigms. Journal of Semantics 10(4), Chierchia, G. (2004). Scalar implicatures, polarity phenomena, and the syntax/pragmatics interface. In A. Belletti (Ed.), Structures and beyond, Volume3,pp Oxford: Oxford University Press. Chierchia, G. (2006). Broaden your views: Implicatures of domain widening and the logicality of language. Linguistic inquiry 37(4), Chierchia, G. (2013). Logic in grammar: Polarity, free choice, and intervention. Oxford: Oxford University Press. Crnic, L. (2011). Getting even. Ph.D.thesis,MIT. Drubig, H. B. (1994). Island constraints and the syntactic nature of focus and association with focus. UniversitätenStuttgartundTübingeninKooperationmitderIBMDeutschlandGmbH. Fauconnier, G. (1975). Polarity and the scale principle. In R. E. Grossman et al. (Ed.), Proceedings of CLS, Volume11,pp Fauconnier, G. (1978). Implication reversal in a natural language. In F. Guenthner and S. J. Schmidt (Eds.), Formal semantics and pragmatics for natural languages, pp Dordrecht: Reidel. 693

23 von Fintel, K. (1999). NPI licensing, strawson entailment, and context dependency. Journal of Semantics 16(2), Gajewski, J. R. (2002). L-analyticity and natural language. Manuscript,MIT. Gajewski, J. R. (2007). Neg-raising and polarity. Linguistics and Philosophy 30(3), Gajewski, J. R. (2011). Licensing strong NPIs. Natural Language Semantics 19(2), Hamblin, C. L. (1973). Questions in Montague English. Foundations of Language 10(1), Heim, I. (1991). Artikel und definitheit. In A. v. Stechow and D. Wunderlich (Ed.), Semantik: ein internationales Handbuch der Zeitgenössischen forschung,pp Berlin:deGruyter. Horn, L. (1969). A presuppositional analysis of only and even. In R. I. Binnick, A. Davison, G. Green, and J. Morgan (Eds.), Proceedings of CLS, Volume5,pp Chicago:CLS. Horn, L. R. (1996). Exclusive company: Only and the dynamics of vertical inference. Journal of Semantics 13(1), Horn, L. R. (2009). Only XL: The assertoric asymmetry of exponibles. In E. Cormany, S. Ito, and D. Lutz (Eds.), Proceedings of SALT, Volume19,pp Klima, E. S. (1964). Negation in English. In J. Fodor and J. Katz (Eds.), The Structure of Language, pp Englewood Cliffs, NJ: Prentice Hall. Krifka, M. (1995). The semantics and pragmatics of polarity items. Linguistic Analysis 25(3-4), Ladusaw, W. A. (1980). Polarity Sensitivity as Inherent Scope Relations.Ph.D.thesis,University of Texas, Austin. Lahiri,U. (1998). Focus and negative polarity in Hindi. Natural Language Semantics 6(1), Rooth, M. (1985). Association with focus. Ph.D.thesis,UniversityofMassachusetts,Amherst. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics 1(1), Rooth, M. (1996). Focus. In S. Lappin (Ed.), The Handbook of Contemporary Semantic Theory, pp Oxford: Blackwell Publishers. Ross, J. R. (1986). Infinite syntax. Norwood:AblexPublishing. Tancredi, C. (1990). Not only EVEN, but even ONLY. Manuscript, MIT. Wagner, M. (2006). Association by movement: Evidence from NPI-licensing. Natural Language Semantics 14(4),